Question: Solve for $x$ and $y$ using substitution. ${-4x+3y = -1}$ ${x = -5y+6}$
Answer: Since $x$ has already been solved for, substitute $-5y+6$ for $x$ in the first equation. ${-4}{(-5y+6)}{+ 3y = -1}$ Simplify and solve for $y$ $20y-24 + 3y = -1$ $23y-24 = -1$ $23y-24{+24} = -1{+24}$ $23y = 23$ $\dfrac{23y}{{23}} = \dfrac{23}{{23}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x = -5y+6}\thinspace$ to find $x$ ${x = -5}{(1)}{ + 6}$ $x = -5 + 6$ ${x = 1}$ You can also plug ${y = 1}$ into $\thinspace {-4x+3y = -1}\thinspace$ and get the same answer for $x$ : ${-4x + 3}{(1)}{= -1}$ ${x = 1}$